Question 389525
a) {{{f(x)=(x^2+x-6)/(x^2+2x-8) = ((x+3)(x-2))/((x+4)(x-2))}}}.  The domain is the set of all real numbers except -4 and 2.  (Determine the domain first before making any cancellations!)

b)There is a vertical asymptote at x = -4.

c)There is a "hole" in the graph at x = 2.

d)After determining the domain and cancelling expressions, we get {{{f(x) = (x+3)/(x+4)}}}.  Y-intercept:  {{{y = f(0) = 3/4}}}.  X-intercept:  {{{0 = (x+3)/(x+4)}}}, which gives x = -3.

e)  The horizontal aymptote: y = 1, found by dividing the top polynomial by the bottom polynomial, OR dividing the highest-degree term of the top polynomial by the highest degree term of the bottom polynomial.